Question

Use a = .01 and conduct a goodness of fit test to see whether the following sample appears to have been selected from a normal distribution.

55, 86, 94, 58, 55, 95, 55, 52, 69, 95, 90, 65, 87, 50, 56 55, 57, 98, 58, 79, 92, 62, 59, 88, 65

a) What is the value of the test statistic?

b) What is the critical value of the test statistic?

c) What is the p-value (or range for the p-value if you are using the tables)

d) What is your decision and conclusion in the context of the problem, i.e., does the data fit the hypothesized distribution or not?

Answer 1

Data sorted in the ascending order:

	x
	50
	52
	55
	55
	55
	55
	56
	57
	58
	58
	59
	62
	65
	65
	69
	79
	86
	87
	88
	90
	92
	94
	95
	95
	98
μ =	71
σ =	17

Hypotheses:

Ho: The data has a come from a normal distribution

Ha: The data has not come from a normal distribution

(a)

Class Interval	Observed f	Expected frequency (as per normal distribution)	(Observed - Expected)^2 /Expected
< 50	0	2.7090	2.7090
50-60	11	3.7609	13.9340
60-70	4	5.4437	0.3829
70-80	1	5.6298	3.8075
80-90	3	4.1600	0.3235
90-98	5	1.8936	5.0962
≥ 98	1	1.4029	0.1157
		chi-square value =	26.3688

Test statistic, χ2 = 26.3688

(b)

Df = 6, α = 0.01, Critical χ2 value = CHIINV(0.01, 6) = 16.8119

(c)

p- value = CHIDIST(26.3688, 6) = 0.0002

(d)

Conclusion: Since 0.0002 < 0.01, reject Ho. The data does not seem to come from a normal distribution.

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